YES Problem: +(0(),y) -> y +(s(x),y) -> s(+(x,y)) -(0(),y) -> 0() -(x,0()) -> x -(s(x),s(y)) -> -(x,y) Proof: DP Processor: DPs: +#(s(x),y) -> +#(x,y) -#(s(x),s(y)) -> -#(x,y) TRS: +(0(),y) -> y +(s(x),y) -> s(+(x,y)) -(0(),y) -> 0() -(x,0()) -> x -(s(x),s(y)) -> -(x,y) Usable Rule Processor: DPs: +#(s(x),y) -> +#(x,y) -#(s(x),s(y)) -> -#(x,y) TRS: Matrix Interpretation Processor: dim=4 usable rules: interpretation: [-#](x0, x1) = [1 0 0 1]x0 + [1 1 1 1]x1, [+#](x0, x1) = [0 1 1 0]x0, [1 0 1 1] [1] [0 0 1 1] [0] [s](x0) = [0 1 1 0]x0 + [1] [1 1 0 1] [0] orientation: +#(s(x),y) = [0 1 2 1]x + [1] >= [0 1 1 0]x = +#(x,y) -#(s(x),s(y)) = [2 1 1 2]x + [2 2 3 3]y + [3] >= [1 0 0 1]x + [1 1 1 1]y = -#(x,y) problem: DPs: TRS: Qed